The Kinks, the Solitons and the Shocks in Series‐Connected Discrete Josephson Transmission Lines

We analytically study the localized running waves in discrete Josephson transmission lines (JTL), constructed from junctions (JJ) and capacitors. The quasi-continuum approximation reduces calculation of wave properties to problem equilibrium an elastic rod potential field. Making additional approximation, we reduce motion fictitious Newtonian particle well. show that there exist form supersonic kinks solitons calculate their velocities profiles. nonstationary smooth which are small perturbations on homogeneous non-zero background described by Korteweg-de Vries equation, those zero – modified equation. also effect dissipation JTL find presence resistors, shunting JJ and/or series with ground capacitors, only possible stationary shock waves, whose profiles found. Finally framework Stocks expansion nonlinear dispersion modulation stability JTL. This article is protected copyright. All rights reserved.